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Simplifying u5 + -13u3 = 36u Reorder the terms: -13u3 + u5 = 36u Solving -13u3 + u5 = 36u Solving for variable 'u'. Reorder the terms: -36u + -13u3 + u5 = 36u + -36u Combine like terms: 36u + -36u = 0 -36u + -13u3 + u5 = 0 Factor out the Greatest Common Factor (GCF), 'u'. u(-36 + -13u2 + u4) = 0Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
Set the factor '(-36 + -13u2 + u4)' equal to zero and attempt to solve: Simplifying -36 + -13u2 + u4 = 0 Solving -36 + -13u2 + u4 = 0 Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + -13u2 + 36 + u4 = 0 + 36 Reorder the terms: -36 + 36 + -13u2 + u4 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13u2 + u4 = 0 + 36 -13u2 + u4 = 0 + 36 Combine like terms: 0 + 36 = 36 -13u2 + u4 = 36 The u term is -13u2. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13u2 + 42.25 + u4 = 36 + 42.25 Reorder the terms: 42.25 + -13u2 + u4 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13u2 + u4 = 78.25 Factor a perfect square on the left side: (u2 + -6.5)(u2 + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (u2 + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
u2 + -6.5 = 8.845903006 Simplifying u2 + -6.5 = 8.845903006 Reorder the terms: -6.5 + u2 = 8.845903006 Solving -6.5 + u2 = 8.845903006 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u2 = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u2 = 8.845903006 + 6.5 u2 = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 u2 = 15.345903006 Simplifying u2 = 15.345903006 Take the square root of each side: u = {-3.917384715, 3.917384715}Subproblem 2
u2 + -6.5 = -8.845903006 Simplifying u2 + -6.5 = -8.845903006 Reorder the terms: -6.5 + u2 = -8.845903006 Solving -6.5 + u2 = -8.845903006 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + u2 = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + u2 = -8.845903006 + 6.5 u2 = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 u2 = -2.345903006 Simplifying u2 = -2.345903006 Reorder the terms: 2.345903006 + u2 = -2.345903006 + 2.345903006 Combine like terms: -2.345903006 + 2.345903006 = 0.000000000 2.345903006 + u2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
u = {0}
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